It takes A 12 days to make a batch of machine parts alone and B 18
days to make them alone. After 6
days of cooperation, A has some
other things to do and left the
rest to be done by B. How many
more days will it take B to
complete the work?
PLEASE EXPLAIN HOW TO SOLVE THIS MY TEACHER WANTS THE WORK
A. 3
B. 5
C. 2
D. 7

Explanation:

Let's say there are 216 machine parts that need to be made. I'm using this number since 12*18 = 216. Refer to the note at the bottom.

If person A works alone, then they can make those 216 parts in 12 days. Person A's unit rate is 216/12 = 18 parts per day.

Person B, working alone, has a rate of 216/18 = 12 parts per day.

If they work together without hindering one another, then their combined unit rate is 18+12 = 30 parts per day.

Working together for 6 days leads to 6*30 = 180 parts made so far. That leaves 216 - 180 = 36 parts left over for person B to finish up.

Since person B does so at a unit rate of 12 parts per day, this means person B needs 36/12 = 3 extra days.

Side note: There's nothing special about the value 216 I picked. I only selected that value so that dividing over 12 and 18 led to whole number results. You could pick the LCM of 12 and 18 to get the same idea.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

the 3rd on is correct

step-by-step explanation: